11/12/2014

11-12-14 - Intel TSX notes

Had a little look at Intel TSX. Some sloppy notes.

TSX are new instructions for (limited) hardware transactions.

I'm gonna talk mainly about the newer RTM (XBEGIN/XEND) because it's conceptually clearer than XACQUIRE/XRELEASE.

In general RTM allows a chunk of speculative code to be run, which can be fully rolled back, and which is not visible to any other core until it is committed. This allows you to do a transaction involving several memory ops, and only commit if there was no contention, so the entire transaction appears atomically to other cores.

The TSX documentation talks about it a lot in terms of "hardware lock elision" (HLE) but it's more general than that. (and HLE the algorithmic process is not to be confused with the annoyingly named "HLE instructions" (XACQUIRE/XRELEASE))

TSX does not gaurantee forward progress, so there must always be a fallback non-TSX pathway. (complex transactions might always abort even without any contention because they overflow the speculation buffer. Even transactions that could run in theory might livelock forever if you don't have the right pauses to allow forward progress, so the fallback path is needed then too).

TSX works by keeping a speculative set of registers and processor state. It tracks all reads done in the speculation block, and enqueues all writes to be delayed until the transaction ends. The memory tracking of the transaction is currently done using the L1 cache and the standard cache line protocols. This means contention is only detected at cache line granularity, so you have the standard "false sharing" issue.

If your transaction reads a cache line, then any write to that cache line by another core causes the transaction to abort. (reads by other cores do not cause an abort).

If your transaction writes a cache line, then any read or write by another core causes the transaction to abort.

If your transaction aborts, then any cache lines written are evicted from L1. If any of the cache lines involved in the transaction are evicted during the transaction (eg. if you touch too much memory, or another core locks that line), the transaction is aborted.

TSX seems to allow quite a large working set (up to size of L1 ?). Obviously the more memory you touch the more likely to abort due to contention.

Obviously you will get aborts from anything "funny" that's not just plain code and memory access. Context switches, IO, kernel calls, etc. will abort transactions.

At the moment, TSX is quite slow, even if there's no contention and you don't do anything in the block. There's a lot of overhead. Using TSX naively may slow down even threaded code. Getting significant performance gains from it is non-trivial.

RTM Memory Ordering :

A successful RTM commit causes all memory operations in the RTM region to appear to execute atomically. A successfully committed RTM region consisting of an XBEGIN followed by an XEND, even with no memory operations in the RTM region, has the same ordering semantics as a LOCK prefixed instruction. The XBEGIN instruction does not have fencing semantics. However, if an RTM execution aborts, all memory updates from within the RTM region are discarded and never made visible to any other logical processor.

One of the best resources is the new Intel Optimization Manual, which has a whole chapter on TSX.

RTM is very nice as a replacement for traditional lockfree algorithms based on atomics when those algorithms are very complex. Something simple like just an atomic increment, you obviously shouldn't use RTM, just do the atomic. Even something like a lockfree LIFO Stack will be better with traditional atomics. But something complex like a lockfree MPMC FIFO Queue will be appropriate for RTM. (an example MPMC FIFO requires two CAS ops, and an atomic load & store, even without contention; so you can replace all those atomic ops with one RTM section which either commits or aborts)

RTM handles nesting in the simplest way - nested transactions are absorbed into their parent. That is, no transaction commits until the topmost parent commits. Aborts in nested transactions will abort the parent.

BEWARE : the transactional code might not need the old fashioned lock-free atomics, but you do still have to be careful about what the optimizer does. Use volatiles, or perhaps relaxed-order atomic stores to make sure that the variable reads/writes you think are happening actually happen where you expect!!


I think an interesting point is that elided locks don't act like normal locks.

Consider a simple object protected by a lock :


struct Thingy
{
    int m_lock; // 0 if unlocked
    int m_a;
    int m_b;
};

The lock provides mutual exclusion for work done on m_a and m_b.

Let's pretend we protected it using a simple spin lock, so a function that used it would be like :


void DoStuff( Thingy * t )
{

while( AtomicExchange(t->m_lock,1) != 0 )
{
  // someone else has the lock; spin :
  pause;
}

// I own the lock
// do stuff to m_a and m_b in here :
DoStuff_Locked(t);

AtomicStore(t->m_lock,0); // release the lock

}

Now we replace it with the RTM transactional version :

void DoStuff( Thingy * t )
{

if ( _xbegin() )
{
  // transactional path

  // add "m_lock" to the transaction read-set :
  if ( t->m_lock != 0 )
  {
    // lock is held, abort transaction
    _xabort();
  }

    // do stuff to m_a and m_b in here :
    DoStuff_Locked(t);

  _xend();
}
else
{
  // transaction aborts go here
  // normal non-transactional path :

    while( AtomicExchange(t->m_lock,1) != 0 )
    {
      // someone else has the lock; spin :
      pause;
    }

    // I own the lock
    // do stuff to m_a and m_b in here :
    DoStuff_Locked(t);

    AtomicStore(t->m_lock,0); // release the lock
}

}

So, how does this work. Let's have a look :

In the transactional path, m_lock is not written to. The lock is not actually held. We do make sure to *read* m_lock so that if another thread takes the lock, it aborts our transaction. Our transaction will only complete if no other thread writes the memory we access.

In fact, the transactional path does not provide mutual exclusion. Multiple threads can read from the same object without conflicting. As lock as the "DoStuff_Locked" only reads, then the transactions will all proceed. In this sense, RTM has converted a normal lock into a read-writer lock!

The transactional path is fine grained! The way we wrote the code is coarse-grained. That is, m_lock protects the entire object, not the individual fields. So if thread 1 tries to modify m_a , and thread 2 modifies m_b, they must wait for each other, even though they are not actually racing. The transactional path will let them both run at the same time, provided there's cache line padding to prevent false sharing.

To be clear :


Transactional :

T1 :
read m_lock
write m_a

T2 :
read m_lock
write m_b

can run simultaneously with no conflict

traditional/fallback lock :

T1 :
take m_lock
write m_a

T2 :
take m_lock
write m_b

must synchronize against each other.

NOTE : as written the transactional path will actually fail all the time, because all the variables are on the same cache line. They need cache-line-size padding between the fields. Perhaps most importantly, the mutex/lock variable that's checked should be on its own cache line that is not written to on the transactional path.

Obviously this doesn't seem too interesting on this little toy object, but on large objects with many fields, it means that operations working on different parts of the object don't synchronize. You could have many threads reading from part of an object while another write writes a different part of the object with no conflict.

It's pretty interesting to me that the elided lock behaves very differently than the original lock. It changes to an RW lock and becomes fine-grained.


Overall I think TSX is pretty cool and I hope it becomes widespread. On the other hand, there is not much real world benefit to most code at the moment.

Some links :

Scaling Existing Lock-based Applications with Lock Elision - ACM Queue
Lock elision in glibc 01.org
TSX anti patterns in lock elision code Intel� Developer Zone
Exploring Intel� Transactional Synchronization Extensions with Intel� Software Development Emulator Intel� Developer Zone
Web Resources about Intel� Transactional Synchronization Extensions Intel� Developer Zone
Fun with Intel� Transactional Synchronization Extensions Intel� Developer Zone

11/11/2014

11-11-14 - x64 movdqa atomic test

How to do an atomic load/store of a 128 bit value on x64 is an ugly question.

The only guaranteed way is via cmpxchg16b. But that's an awfully slow way to do a load or store.

movdqa appears to be an atomic way to move 128 bits - on most chips. Not all. And Intel/AMD don't want to clearly identify the cases where it is atomic or not. (they specifically don't guarantee it)

At the moment, shipping code needs to use cmpx16 to be safe. (my tests indicate that the x64 chips in the modern game consoles *do* have atomic movdqa, so it seems safe to use there)

My main curiousity is whether there exist any modern ("Core 2" or newer) x64 chips that *do not* provide an atomic movdqa.

Anyhoo, here's a test to check if movdqa is atomic on your machine. If you like, run it and send me the results : (Windows, x64 only)

cb_x64_atomics_test.7z

The atomic test will just run for a while. If it has a failure it will break.

(you will get some errors about not having a v: or r: drive; you can just ignore them.)

Copy the output, or should be able to get the log file here :

"c:\oodlelogs\oodle_cb_test_x64_atomics.log"
"c:\oodlelogs\oodle_cb_test_x64_atomics.prev"

email me at cb at my domain.


For the record, an atomic 128 bit load/store for x64 Windows using cmpx16 :


#include <intrin.h>

void AtomicLoad128(__int64 * out_Result, __int64 volatile * in_LoadFrom)
{
    // do a swap of the value in out_Result to itself
    //  if it matches, it stays the same
    //  it it doesn't match, we get a load
    _InterlockedCompareExchange128(in_LoadFrom,out_Result[1],out_Result[0],out_Result);
}

void AtomicStore128(__int64 volatile * out_StoreTo,const __int64 * in_Value)
{
    // do an initial non-atomic load of StoreTo :
    __int64 check_StoreTo[2];
    check_StoreTo[0] = out_StoreTo[0];
    check_StoreTo[1] = out_StoreTo[1];
    // store with cmpx16 :
    while( ! _InterlockedCompareExchange128(out_StoreTo,in_Value[1],in_Value[0],check_StoreTo) )
    {
        // check_StoreTo was reloaded with the value in out_StoreTo
        _mm_pause();
    }
}

9/10/2014

09-10-14 - Suffix Trie EOF handling

I realized something.

In a Suffix Trie (or suffix sort, or anything similar), handling the end-of-buffer is a mess.

The typical way it's described in the literature is to treat the end-of-buffer (henceforth EOB) as if it is a special character with value out of range (such as -1 or 256). That way you can just compare strings that go up to EOB with other strings, and the EOB will always mismatch a normal character and cause those strings to sort in a predictable way.

eg. on "banana" when you insert the final "na-EOB" you compare against "nana" and wind up comparing EOB vs. 'n' to find the sort order for that suffix.

The problem is that this is just a mess in the code. All over my suffix trie code, everywhere that I do a string lookup, I had to do extra special case checking for "is it EOB" and handle that case.

In addition, when I find a mismatch of "na-EOB" and "nan", the normal path of the code would be to change the prefix "na" into a branch and add children for the two different paths - EOB and "n". But I can't actually do that in my code because the child is selected by an unsigned char (uint8), and EOB is out of bounds for that variable type. So in all the node branch construction paths I have to special case "is it a mismatch just because of EOB, then don't create a branch". Blah blah.

Anyway, I realized that can all go away.

The key point is this :

Once you add a suffix that hits EOB (eg. the first mismatch against the existing suffixes is at EOB), then all future suffixes will also hit EOB, and that will be the deepest match for all of them.

Furthermore, all future suffix nodes can be found immediately using "follows"

eg. in the "banana" case, construction of the trie goes like :


"ban" is in the suffix trie
  (eg. "ban..","an..","n.." are all in the trie)

add "ana" :

we find the existing "an.."

the strings we compare are "anana-EOB" vs "ana-EOB"

so the mismatch hits EOB

That means all future suffixes will also hit EOB, and their placement in the tree can be found
just by using "follows" from the current string.

"ana-EOB" inserts at "anana"
"na-EOB" inserts at "nana"
"a-EOB" inserts at "ana"

That is, at the end of every trie construction when you start hitting EOB you just jump out to this special case of very simple follows addition.

So all the special EOB handling can be pulled out of the normal Trie code and set off to the side, which is lovely for the code clarity.

In practice it's quite common for files to end with a run of "000000000" which now gets swallowed up neatly by this special case.


ADD : if you don't care about adding every occurance of each suffix, then it gets even simpler -

If you hit EOB when adding a string - just don't add it. A full match of that suffix already exists, and your suffix that goes to EOB can't match any lookup better than what's in there.

(note that when I say "hit EOB" I mean you are at a branch node, and your current character doesn't match any of the branches because it is EOB. You will still add leaves that go to EOB, but you will never actually walk down those leaves to reach EOB.)

8/31/2014

08-31-14 - DLI Image Compression

I got pinged about DLI so I had a look.

DLI is a closed source image compressor. There's no public information about it. It may be the best lossy image compressor in the world at the moment.

(ASIDE : H265 looks promising but has not yet been developed as a still image compressor; it will need a lot of perceptual work; also as in my previous test of x264 you have to be careful to avoid the terrible YUV and subsamplers that are in the common tools)

I have no idea what the algorithms are in DLI. Based on looking at some of the decompressed images, I can see block transform artifacts, so it has something like an 8x8 DCT in it. I also see certain clues that make me think it uses something like intra prediction. (those clues are good detail and edge preservation, and a tendency to preserve detail even if it's the wrong detail; the same thing that you see in H264 stills)

Anyway, I thought I'd run my own comparo on DLI to see if it really is as good as the author claims.

I tested against JPEG + packJPEG + my JPEG decoder. I'm using an unfinished version of my JPEG decoder which uses the "Nosratinia modified" reconstruction method. It could be a lot better. Note that this is still a super braindead simple JPEG. No per-block quantizer. No intra prediction. Only 8x8 transforms. Standard 420 YCbCr. No trellis quantization or rate-distortion. Just a modern entropy coding back end and a modern deblocking decoder.

I test with my perceptual image tester imdiff . The best metric is Combo which is a linear combo of SCIELAB_MyDelta + MS_SSIM_IW_Y + MyDctDelta_YUV.

You can see some previous tests on mysoup or moses or PDI

NOTE : "dlir.exe" is the super-slow optimizing variant. "dli.exe" is reasonably fast. I tested both. I ran dlir with -ov (optimize for visual quality) since my tests are mostly perceptual. I don't notice a huge difference between them.

My impressions :

DLI and jpeg+packjpg+jpegdec are both very good. Both are miles ahead of what is commonly used these days (old JPEG for example).

DLI preserves detail and contrast much better. JPEG tends to smooth and blur things at lower bit rates. Part of this may be something like a SATD heuristic metric + better bit allocation.

DLI does "mangle" the image. That is, it gets the detail *wrong* sometimes, which is something that JPEG really never does. The primary shapes are preserved by jpeg+packjpg+jpegdec, they just lose detail. With DLI, you sometimes get weird lumps appearing that weren't there before. If you just look at the decompressed image it can be hard to spot, because it looks like there's good detail there, but if you A-B test the uncompressed to the original, you'll see that DLI is actually changing the detail. I saw this before when analyzing x264.

DLI is similar looking to x264-still but better.

DLI seems to have a special mode for gradients. It preserves smooth gradients very well. JPEG-unblock creates a stepped look because it's a series of ramps that are flat in the middle.

DLI seems to make edges a bit chunky. Smooth curves get steppy. jpeg+packjpg+jpegdec is very good at preserving a smooth curved edge.

DLI is the only image coder I've seen that I would say is definitely slightly better than jpeg+packjpg+jpegdec. Though it is worse in some ways, I think the overall impression of the decoded image is definitely better. Much better contrast preservation, much better detail energy level preservation.

Despite jpeg often scoring better than DLI on the visual quality metrics I have, DLI usually looks much better to my eyes. This is a failure of the visual quality metrics.


Okay. Time for some charts.

In all cases I will show the "TID Fit" score. This is a 0-10 quality rating with higher better. This removes the issue of SSIM, RMSE, etc. all being on different scales.

NOTE : I am showing RMSE just for information. It tells you something about how the coders are working and why they look different, where the error is coming from. In both cases (DLI and JPEG) the runs are optimized for *visual* quality, not for RMSE, so this is not a comparison of how well they can do on an RMSE contest. (dlir should be run with -or and jpeg should be run with flat quantization matrices at least).

(see previous tests on mysoup or moses or PDI )

mysoup :

moses :

porsche640 :

pdi1200 :


Qualitative Comparison :

I looked at JPEG and DLI encodings at the same bit rate for each image. Generally I try to look around 1 bpp (that's logbpp of 0) which is the "sweet spot" for lossy image compression comparison.

Here are the original, a JPEG, and a DLI of Porsche640.
Download : RAR of Porsche640 comparison images (1 MB)

What I see :

DLI has very obvious DCT ringing artifacts. Look at the lower-right edge of the hood, for example. The sharp line of the hood has ringing ghosts in 8x8 chunks.

DLI preserves contrast overall much better. The most obvious places are in the background - the leaves, the pebbles. JPEG just blurs those and drops a lot of high frequency detail, DLI keeps it much better. DLI preserves a lot more high frequency data.

DLI adds a lot of noise. JPEG basically never adds noise. For example compare the centers of the wheels. The JPEG just looks like a slightly smoothed version of the original. The DLI has got lots of chunkiness and extra variation that isn't in the original.

In a few places DLI really mangles the image. One is the A-pillar of the car, another is the shadow on the hood, also the rear wheel.

Both DLI and JPEG do the same awful thing to the chroma. All the orange in the gravel is completely lost. The entire color of the laurel bush in the background is changed. Both just produce a desaturated image.

Based on the scores and what I see perceptually, my guess is this : DLI uses an 8x8 DCT. It uses a quantization matrix that is much flatter than JPEG's.

8/27/2014

08-27-14 - LZ Match Length Redundancy

A quick note on something that does not work.

I've written before about the redundancy in LZ77 codes. ( for example ). In particular the issue I had a look at was :

Any time you code a match, you know that it must be longer than any possible match at lower offsets.

eg. you won't sent a match of length of 3 to offset 30514 if you could have sent offset 1073 instead. You always choose the lowest possible offset that gives you a given match length.

The easy way to exploit this is to send match lengths as the delta from the next longest match length at lower offset. You only need to send the excess, and you know the excess is greater than zero. So if you have an ML of 3 at offset 1073, and you find a match of length 4 at offset 30514, then you send {30514,+1}

To implement this in the encoder is straightforward. If you walk your matches in order from lowest offset to highest offset, then you know the current best match length as you go. You only consider a match if it exceeds the previous best, and you record the delta in lengths that you will send.

The same principle applies to the "last offsets" ; you don't send LO2 if you could sent LO0 at the same length, so the higher index LO matches must be of greater length. And the same thing applies to ROLZ.

I tried this in all 3 cases (normal LZ matches, LO matches, ROLZ). No win. Not even tiny, but close to zero.

Part of the problem is that match lengths are just not where the bits are; they're small already. But I assume that part of what's happening is that match lengths have patterns that the delta-ing ruins. For example binary files will have patterns of 4 or 8 long matches, or in an LZMA-like you'll have certain patterns show up like at certain pos&3 intervals after a literal you get a 3-long match, etc.

I tried some obvious ideas like using the next-lowest-length as part of the context for coding the delta-length. In theory you could be able to recapture something like a next-lowest of 3 predicts a delta of 1 in places where an ML of 4 is likely. But I couldn't find a win there.

I believe this is a dead end. Even if you could find a small win, it's too slow in the decoder to be worth it.

7/14/2014

07-14-14 - Suffix-Trie Coded LZ

Idea : Suffix-Trie Coded LZ :

You are doing LZ77-style coding (eg. matches in the prior stream or literals), but send the matches in a different way.

You have a Suffix Trie built on the prior stream. To find the longest match for a normal LZ77 you would take the current string to code and look it up by walking it down the Trie. When you reach the point of deepest match, you see what string in the prior stream made that node in the Trie, and send the position of that string as an offset.

Essentially what the offset does is encode a position in the tree.

But there are many redundancies in the normal LZ77 scheme. For example if you only encode a match of length 3, then the offsets that point to "abcd.." and "abce.." are equivalent, and shouldn't be distinguished by the encoding. The fact that they both take up space in the numerical offset is a waste of bits. You only want to distinguish offsets that actually point at something different for the current match length.

The idea in a nutshell is that instead of sending an offset, you send the descent into the trie to find that string.

At each node, first send a single bit for does the next byte in the string match any of the children. (This is equivalent to a PPM escape). If not, then you're done matching. If you like, this is like sending the match length with unary : 1 bits as long as you're in a node that has a matching child, then a 0 bit when you run out of matches. (alternatively you could send the entire match length up front with a different scheme).

When one of the children matches, you must encode which one. This is just an encoding of the next character, selected from the previously seen characters in this context. If all offsets are equally likely (they aren't) then the correct thing is just Probability(child) = Trie_Leaf_Count(child) , because the number of leaves under a node is the number of times we've seen this substring in the past.

(More generally the probability of offsets is not uniform, so you should scale the probability of each child using some modeling of the offsets. Accumulate P(child) += P(offset) for each offset under a child. Ugly. This is unfortunately very important on binary data where the 4-8-struct offset patterns are very strong.)

Ignoring that aside - the big coding gain is that we are no longer uselessly distinguishing offsets that only differ at higher match length, AND instead of just wasting those bits, we instead use them to make those offsets code smaller.

For example : say we've matched "ab" so far. The previous stream contains "abcd","abce","abcf", and "abq". Pretend that somehow those are the only strings. Normal LZ77 needs 2 bits to select from them - but if our match len is only 3 that's a big waste. This way we would say the next char in the match can either be "c" or "q" and the probabilities are 3/4 and 1/4 respectively. So if the length-3 match is a "c" we send that selection in only log2(4/3) bits = 0.415

And the astute reader will already be thinking - this is just PPM! In fact it is exactly a kind of PPM, in which you start out at low order (min match length, typically 3 or so) and your order gets deeper as you match. When you escape you junk back to order 3 coding, and if that escapes it jumps back to order 0 (literal).

There are several major problems :

1. Decoding is slow because you have to maintain the Suffix Trie for both encode and decode. You lose the simple LZ77 decoder.

2. Modern LZ's benefit a lot from modeling the numerical value of the offset in binary files. That's ugly & hard to do in this framework. This method is a lot simpler on text-like data that doesn't have numerical offset patterns.

3. It's not Pareto. If you're doing all this work you may as well just do PPM.

In any case it's theoretically interesting as an ideal of how you would encode LZ offsets if you could.

(and yes I know there have been many similar ideas in the past; LZFG of course, and Langdon's great LZ-PPM equivalence proof)

7/03/2014

07-03-14 - Oodle 1.41 Comparison Charts

I did some work for Oodle 1.41 on speeding up compressors. Mainly the Fast/VeryFast encoders got faster. I also took a pass at trying to make sure the various options were "Pareto", that is the best possible space/speed tradeoff. I had some options that were off the curve, like much slower than they needed to be, or just worse with no benefit, so it was just a mistake to use them (LZNib Normal was particularly bad).

Oodle 1.40 got the new LZA compressor. LZA is a very high compression arithmetic-coded LZ. The goal of LZA is as much compression as possible while retaining somewhat reasonable (or at least tolerable) decode speeds. My belief is that LZA should be used for internet distribution, but not for runtime loading.

The charts :

compression ratio : (raw/comp ratio; higher is better)

compressor VeryFast Fast Normal Optimal1 Optimal2
LZA 2.362 2.508 2.541 2.645 2.698
LZHLW 2.161 2.299 2.33 2.352 2.432
LZH 1.901 1.979 2.039 2.121 2.134
LZNIB 1.727 1.884 1.853 2.079 2.079
LZBLW 1.636 1.761 1.833 1.873 1.873
LZB16 1.481 1.571 1.654 1.674 1.674
lzmamax  : 2.665 to 1
lzmafast : 2.314 to 1
zlib9 : 1.883 to 1 
zlib5 : 1.871 to 1
lz4hc : 1.667 to 1
lz4fast : 1.464 to 1

encode speed : (mb/s)

compressor VeryFast Fast Normal Optimal1 Optimal2
LZA 23.05 12.7 6.27 1.54 1.07
LZHLW 59.67 19.16 7.21 4.67 1.96
LZH 76.08 17.08 11.7 0.83 0.46
LZNIB 182.14 43.87 10.76 0.51 0.51
LZBLW 246.83 49.67 1.62 1.61 1.61
LZB16 511.36 107.11 36.98 4.02 4.02
lzmamax  : 5.55
lzmafast : 11.08
zlib9 : 4.86
zlib5 : 25.23
lz4hc : 32.32
lz4fast : 606.37

decode speed : (mb/s)

compressor VeryFast Fast Normal Optimal1 Optimal2
LZA 34.93 37.15 37.76 37.48 37.81
LZHLW 363.94 385.85 384.83 391.28 388.4
LZH 357.62 392.35 397.72 387.28 383.38
LZNIB 923.66 987.11 903.21 1195.66 1194.75
LZBLW 2545.35 2495.37 2465.99 2514.48 2515.25
LZB16 2752.65 2598.69 2687.85 2768.34 2765.92
lzmamax  : 42.17
lzmafast : 40.22
zlib9 : 308.93
zlib5 : 302.53
lz4hc : 2363.75
lz4fast : 2288.58

While working on LZA I found some encoder speed wins that I ported back to LZHLW (mainly in Fast and VeryFast). A big one is to early out for last offsets; when I get a last offset match > N long, I just take it and don't even look for non-last-offset matches. This is done in the non-Optimal modes, and surprisingly hurts compression almost not all while helping speed a lot.

Four of the compressors are now in pretty good shape (LZA,LZHLW,LZNIB, and LZB16). There are a few minor issues to fix someday (someday = never unless the need arises) :

LZA decoder should be a little faster (currently lags LZMA a tiny bit). LZA Optimal1 would be better with a semi-greedy match finder like MMC (LZMA is much faster to encode than me at the same compression level; perhaps a different optimal parse scheme is needed too). LZA Optimal2 should seed with multi-parse. LZHLW Optimal could be faster. LZNIB Normal needs much better match selection heuristics, the ones I have are really just not right. LZNIB Optimal should be faster; needs a better way to do threshold-match-finding. LZB16 Optimal should be faster; needs a better 64k-sliding-window match finder.

The LZH and LZBLW compressors are a bit neglected and you can see they still have some of the anomalies in the space/speed tradeoff curve, like the Normal encode speed for LZBLW is so bad that you may as well just use Optimal. Put aside until there's a reason to fix them.


If another game developer tells me that "zlib is a great compromise and you probably can't beat it by much" I'm going to murder them. For the record :

zlib -9 :
4.86 MB/sec to encode
308.93 MB/sec to decode
1.883 to 1 compression

LZHLW Optimal1 :
4.67 MB/sec to encode
391.28 MB/sec to decode
2.352 to 1 compression
come on! The encoder is slow, the decoder is slow, and it compresses poorly.

LZMA in very high compression settings is a good tradeoff. In its low compression fast modes, it's very poor. zlib has the same flaw - they just don't have good encoders for fast compression modes.

LZ4 I have no issues with; in its designed zone it offers excellent tradeoffs.


In most cases the encoder implementations are :


VeryFast =
cache table match finder
single hash
greedy parse

Fast = 
cache table match finder
hash with ways
second hash
lazy parse
very simple heuristic decisions

Normal =
varies a lot for the different compressors
generally something like a hash-link match finder
or a cache table with more ways
more lazy eval
more careful "is match better" heuristics

Optimal =
exact match finder (SuffixTrie or similar)
cost-based match decision, not heuristic
backward exact parse of LZB16
all others have "last offset" so require an approximate forward parse

I'm mostly ripping out my Hash->Link match finders and replacing them with N-way cache tables. While the cache table is slightly worse for compression, it's a big speed win, which makes it better on the space-speed tradeoff spectrum.

I don't have a good solution for windowed optimal parse match finding (such as LZB16-Optimal). I'm currently using overlapped suffix arrays, but that's not awesome. Sliding window SuffixTrie is an engineering nightmare but would probably be good for that. MMC is a pretty good compromise in practice, though it's not exact and does have degenerate case breakdowns.


LZB16's encode speed is very sensitive to the hash table size.


-h12
24,700,820 ->16,944,823 =  5.488 bpb =  1.458 to 1
encode           : 0.045 seconds, 161.75 b/kc, rate= 550.51 mb/s
decode           : 0.009 seconds, 849.04 b/kc, rate= 2889.66 mb/s

-h13
24,700,820 ->16,682,108 =  5.403 bpb =  1.481 to 1
encode           : 0.049 seconds, 148.08 b/kc, rate= 503.97 mb/s
decode           : 0.009 seconds, 827.85 b/kc, rate= 2817.56 mb/s

-h14
24,700,820 ->16,491,675 =  5.341 bpb =  1.498 to 1
encode           : 0.055 seconds, 133.07 b/kc, rate= 452.89 mb/s
decode           : 0.009 seconds, 812.73 b/kc, rate= 2766.10 mb/s

-h15
24,700,820 ->16,409,957 =  5.315 bpb =  1.505 to 1
encode           : 0.064 seconds, 113.23 b/kc, rate= 385.37 mb/s
decode           : 0.009 seconds, 802.46 b/kc, rate= 2731.13 mb/s

If you accidentally set it too big you get a huge drop-off in speed. (The charts above show -h13 ; -h12 is more comparable to lz4fast (which was built with HASH_LOG=12)).

I stole an idea from LZ4 that helped the encoder speed a lot. (lz4fast is very good!) Instead of doing the basic loop like :


while(!eof)
{
  if ( match )
    output match
  else
    output literal
}

instead do :

while(!eof)
{
  while( ! match )
  {
    output literal
  }

  output match
}

This lets you make a tight loop just for outputing literals. It makes it clearer to you as a programmer what's happening in that loop and you can save work and simplify things. It winds up being a lot faster. (I've been doing the same thing in my decoders forever but hadn't done in the encoder).

My LZB16 is very slightly more complex to encode than LZ4, because I do some things that let me have a faster decoder. For example my normal matches are all no-overlap, and I hide the overlap matches in the excess-match-length branch.

6/21/2014

06-21-14 - Suffix Trie Note

A small note on Suffix Tries for LZ compression.

See previously :

Sketch of Suffix Trie for Last Occurance

So. Reminder to myself : Suffix Tries for optimal parsing is clean and awesome. But *only* for finding the length of the longest match. *not* for finding the lowest offset of that match. And *not* for finding the longest match length and the lowest offset of any other (shorter) matches.

I wrote before about the heuristic I currently use in Oodle to solve this. I find the longest match in the trie, then I walk up to parent nodes and see if they provide lower offset / short length matches, because those may be also interesting to consider in the optimal parser.

(eg. for clarity, the situation you need to consider is something like a match of length 8 at offset 482313 vs. a match of length 6 at offset 4 ; it's important to find that lower-length lower-offset match so that you can consider the cost of it, since it might be much cheaper)

Now, I tested the heuristic of just doing parent-gathers and limitted updates, and it performed well *in my LZH coder*. It does *not* necessarily perform well with other coders.

It can miss out on some very low offset short matches. You may need to supplement the Suffix Trie with an additional short range matcher, like even just a 1024 entry hash-chain matcher. Or maybe a [256*256*256] array of the last occurance location of a trigram. Even just checking at offset=1 for the RLE match is helpful. Whether or not they are important or not depends on the back end coder, so you just have to try it.

For LZA I ran into another problem :

The Suffix Trie exactly finds the length of the longest match in O(N). That's fine. The problem is when you go up to the parent nodes - the node depth is *not* the longest match length with the pointer there. It's just the *minimum* match length. The true match length might be anywhere up to *and including* the longest match length.

In LZH I was considering those matches with the node depth as the match length. And actually I re-tested it with the correct match length, and it makes very little difference.

Because LZA does LAM exclusion, it's crucial that you actually find what the longest ML is for that offset.

(note that the original LZMA exclude coder is actually just a *statistical* exclude coder; it is still capable of coding the excluded character, it just has very low probability. My modified version that only codes 7 bits instead of 8 is not capable of coding the excluded character, so you must not allow this.)

One bit of ugliness is that extending the match to find its true length is not part of the neat O(N) time query.

In any case, I think is all a bit of a dead-end for me. I'd rather move my LZA parser to be forward-only and get away from the "find a match at every position" requirement. That allows you to take big steps when you find long matches and makes the whole thing faster.

6/18/2014

06-18-14 - Oodle Network Test Results

Well, it's been several months now that we've been testing out the beta of Oodle Network Compression on data from real game developers.

Most of the tests have been UDP, with a few TCP. We've done a few tests on data from the major engines (UE3/4, Source) that do delta property bit-packing. Some of the MMO type games with large packets were using zlib on packets.

This is a summary of all the major tests that I've run. This is not excluding any tests where we did badly. So far we have done very well on every single packet capture we've seen from game developers.


MMO game :
427.0 -> 182.7 average = 2.337:1 = 57.21% reduction
compare to zlib -5 : 427.0 -> 271.9 average


MMRTS game :
122.0 -> 75.6 average = 1.615:1 = 38.08% reduction


Unreal game :
220.9 -> 143.3 average = 1.542:1 = 35.15% reduction


Tiny packet game :
21.9 -> 15.6 average = 1.403:1 = 28.72% reduction


Large packet Source engine game :
798.2 -> 519.6 average = 1.536:1 = 34.90% reduction

Some of the tests surprised even me, particularly the tiny packet one. When I saw the average size was only 22 bytes I didn't think we had much room to work with, but we did!

Some notes :

  • Oodle Network Compression provides > 28% reduction in all cases seen so far.

  • Oodle works even on tiny packets!

  • Oodle greatly out-compresses zlib. Some developers think that zlib is a great compromise for space and speed. Oodle can do much better! Oodle is also generally faster to encode than zlib and uses less memory per channel.

  • Oodle works even on games that are already doing bit-packing and delta updates (like most of the major traditional engines do).

  • Oodle easily pays for itself; the savings in bandwidth is much greater than the cost of Oodle. In addition to the cost savings, Oodle means you can run more players

6/16/2014

06-16-14 - Rep0 Exclusion in LZMA-like coders

For reference on this topic : see the last post .

I believe there's a mistake in LZMA. I could be totally wrong about that because reading the 7z code is very hard; in any case I'm going to talk about Rep0 exclusion. I believe that LZMA does not do this the way it should, and perhaps this change should be integrated into a future version. In general I have found LZMA to be very good and most of its design decisions have been excellent. My intention is not to nitpick it, but to give back to a very nice algorithm which has been generously made public by its author, Igor Pavlov.

LZMA does "literal-after-match" exclusion. I talked a bit about this last time. Basically, after a match you know that the next literal cannot be the one that would have continued the match. If it was you would have just written a longer match. This relies on always writing the maximum length for matches.

To model "LAM" exclusion, LZMA uses a funny way of doing the binary arithmetic model for those symbols. I wrote a bit about that last time, and the LZMA way to do that is good.

LZMA uses LAM exclusion on the first literal after a match, and then does normal 8-bit literal coding if there are more literals.

That all seems fine, and I worked on the Oodle LZ-Arith variant for about month with a similar scheme, thinking it was right.

But there's a wrinkle. LZMA also does "rep0len1" coding.

For background, LZMA, like LZX before it, does "repeat match" coding. A rep match means using one of the last N offsets (usually N = 3) and you flag that and send it in very few bits. I've talked about the surprising importance of repeat matches before (also here and other places ).

LZMA, like LZX, codes rep matches with MML of 2.

But LZMA also has "rep0len1". rep0len1 codes a single symbol at the 0th repeat match offset. That's the last offset matched from. That's the same offset that provides the LAM exclusion. In fact you can state the LAM exclusion as "rep0len1 cannot occur on the symbol after a match". (and in fact LZMA gets that right and doesn't try to code the rep0len1 bit after a match).

rep0len1 is not a win on text, but it's a decent little win on binary structured data (see example at bottom of this post ). It lets you get things like the top byte of a series of floats (off=4 len1 match, then 3 literals).

The thing is, if you're doing the rep0len1 coding, then normal literals also cannot be the rep0len1 symbol. If they were, then you would just code them with the rep0len1 flag.

So *every* literal should be coded with rep0 exclusion. Not just the literal after a match. And in fact the normal 8-bit literal coding path without exclusion is never used.

To be concrete, coding a literal in LZMA should look like this :


cur_lit = buffer[ pos ];

rep0_lit = buffer[ pos - rep0_offset ];

if ( after match )
{
    // LAM exclusion means cur_lit should never be = rep0_lit
    ASSERT( cur_lit != rep0_lit );
}
else
{
    if ( cur_lit == rep0_lit )
    {
        // lit is rep0, send rep0len1 :
        ... encode rep0len1 flag ...

        // do not drop through
        return;
    }
}

// either way, we now have exclusion :
ASSERT( cur_lit != rep0_lit );

encode_with_exclude( cur_lit, rep0_lit );

and that provides a pretty solid win. Of all the things I did to try to beat LZMA, this was the only clear winner.


ADDENDUM : some notes on this.

Note that the LZMA binary-exclude coder is *not* just doing exclusion. It's also using the exclude symbol as modelling context. Pure exclusion would just take the probability of the excluded symbol and distribute it to the other symbols, in proportion to their probability.

It turns out that the rep0 literal is an excellent predictor, even beyond just exclusion.

That is, say you're doing normal 8-bit literal coding with no exclusion. You are allowed to use an 8-bit literal as context. You can either use the order-1 literal (that's buffer[pos-1]) or the rep0 literal (that's buffer[pos-rep0_offset]).

It's better to use the rep0 literal!

Of course the rep0 literal becomes a weaker predictor as you get away from the end of the match. It's very good on the literal right after a match (lam exclusion), and still very good on the next literal, and then steadily weaker.

It turns out the transition point is 4-6 literals away from the end of the match; that's the point at which the o1 symbol becomes more correlated to the current symbol than the rep0 lit.

One of the ideas that I had for Oodle LZA was to remove the rep0len1 flag completely and instead get the same effect from context modeling. You can instead take the rep0 lit and use it as an 8-bit context for literal coding, and should get the same benefit. (the coding of the match flag is implicit in the probability model).

I believe the reason I couldn't find a win there is because it turns out that LZ literal coding needs to adapt very fast. You want very few context bits, you want super fast adaptation of the top bits. Part of the issue is that you don't see LZ literals very often; there are big gaps where you had matches, so you aren't getting as much data to adapt to the file. But I can't entirely explain it.

You can intuitively understand why the rep0 literal is such a strong predictor even when it doesn't match. You've taken a string from earlier in the file, and blacked out one symbol. You're told what the symbol was before, and you're told that in the new string it is not that symbol. It's something like :


"Ther" matched before
'r' is to be substituted
"The?"
What is ? , given that it was 'r' but isn't 'r' here.

Given only the o1 symbol ('e') and the substituted symbol ('r'), you can make a very good guess of what should be there ('n' probably, maybe 'm', or 's', ...). Obviously more context would help, but with limited information, the substituted symbol (rep0 lit) sort of gives you a hint about the whole area.

An ever simpler case is given just the fact that rep0lit is upper or lower case - you're likely to substitute it with a character of the same case. Similarly if it's a vowel or consonant, you're likely to substitute with one of the same. etc. and of course I'm just using English text because it's intuitive, it works just as well on binary structured data.


There's another very small flaw in LZMA's exclude coder, which is more of a minor detail, but I'll include it here.

The LZMA binary exclude coder is equivalent to this clearer version that I posted last time :


void BinaryArithCodeWithExclude( ArithEncoder * arith, int val, int exclude )
{
    int ctx = 1; // place holder top bit

    // first loop in the "matched" part of the tree :
    for(;;)
    {
        int exclude_bit = (exclude >> 7) & 1; exclude <<= 1;
        int bit = (val >> 7) & 1; val <<= 1;
        ASSERT( ctx < 256 );
        m_bins[256 + ctx + (exclude_bit<<8)].encode(arith,bit);
        ctx = (ctx<<1) | bit;
        if ( ctx >= 256 )
            return;
        if ( bit != exclude_bit )
            break;
    }
    
    // then finish bits that are unmatched :
    // non-matched
    do
    {
        int bit = (val >> 7) & 1; val <<= 1;
        m_bins[ctx].encode(arith,bit);
        ctx = (ctx<<1) | bit;
    }
    while( ctx < 256 );
}
This codes up to 8 bits while the bits of "val" match the bits of "exclude" , and up to 8 bits while the bits of "val" don't match.

Now, obviously the very first bit can never be coded in the unmatched phase. So we could eliminate that from the unmatched bins. But that only saves us one slot.

(and actually I'm already wasting a slot intentionally; the "ctx" with place value bit like this is always >= 1 , so you should be indexing at "ctx-1" if you want a tight packed array. I intentionally don't do that, so that I have 256 bins instead of 255, because it makes the addressing work with "<<8" instead of "*255")

More importantly, in the "matched" phase, you don't actually need to code all 8 bits. If you code 7 bits, then you know that "val" and "exclude" match in all top 7 bits, so it must be that val == exclude^1. That is, it's just one bit flip away; the decoder will also know that so you can just not send it.

The fixed encoder is :


void BinaryArithCodeWithExclude( ArithEncoder * arith, int val, int exclude )
{
    int ctx = 1; // place holder top bit

    // first loop in the "matched" part of the tree :
    for(;;)
    {
        int exclude_bit = (exclude >> 7) & 1; exclude <<= 1;
        int bit = (val >> 7) & 1; val <<= 1;
        ASSERT( ctx < 128 );
        m_bins[256 + ctx + (exclude_bit<<7)].encode(arith,bit);
        ctx = (ctx<<1) | bit;
        if ( bit != exclude_bit )
            break;
        if ( ctx >= 128 )
        {
            // I've coded 7 bits
            // and they all match
            // no need to code the last one
            return;
        }
    }
    
    // then finish bits that are unmatched :
    // non-matched
    do
    {
        int bit = (val >> 7) & 1; val <<= 1;
        m_bins[ctx].encode(arith,bit);
        ctx = (ctx<<1) | bit;
    }
    while( ctx < 256 );
}
Note that now ctx in the matched phase can only reach 128. That means this coder actually only needs 2*256 bins, not 3*256 bins as stated last time.

This is a little speed savings (tiny because we only get one less arith coding event on a rare path), a little compression savings (tiny because that bottom bit models very well), and a little memory use savings.

old rants